Hadronic structure on the light front. IX. Orbital-spin-isospin wave functions of baryons

This paper, which is part of a series, is devoted to several technical issues. In the first part of the paper, we discuss the usual wave functions in the center of mass frame for baryons, by clarifying the representations of the three-quark permutation group S₃. We extend the analysis for up to five ``spinors'' with ρ, λ-symmetry, and derive explicitly the totally symmetric wave functions modulo color. They are explicitly used to describe the excited nucleons N* states, in the P- and D-shell. We also show how to use symbolic operations in Mathematica, in spin-tensor notations to make explicit these states. For the S- and P-shells, the totally antisymmetric wave functions are given, and the pertinent matrix elements for the spin-dependent operators calculated, including the mixing between states with different total spin S. In the second part of the paper we turn to the light front wave functions, with an emphasis on the longitudinal wave functions, with a novel basis set. We also discuss their symmetries under permutations, and select the proper combinations for the transverse and longitudinal excitations for N* on the light front.